从林德布拉德动力学看泡利噪声的对称性
Symmetries of Pauli Noise from Lindbladian Dynamics
AI总结：
本文利用林德布拉德微扰理论分析量子门噪声的泡利保真度对称性，证明相干误差不引起一阶不对称，而特定耗散误差可打破对称性，并利用该对称性固定规范以识别SPAM误差。
AI中文摘要：
表征量子电路中的噪声从根本上受到规范自由度的限制；某些参数，例如状态制备和测量（SPAM）误差的各自贡献，原则上无法从门集内的任何实验中学习。在这里，我们表明实际噪声过程的物理结构对门噪声通道的泡利保真度施加了近似对称约束。这些对称性将泡利 $P$ 的保真度与其门共轭 $U_g P U_g ^{\dagger}$ 的保真度联系起来，并且可以仅使用误差类型而非其大小的知识来固定规范。利用林德布拉德微扰理论，我们分析了一大类克利福德门，包括 $ZZ_{\pi/2}$、CZ、CNOT、iSWAP 和 SWAP，并证明相干误差不会引起一阶不对称，而只有一组受限的主要是非对角耗散误差才能在一阶打破对称性，为此我们推导了简单的选择规则。值得注意的是，常见的单量子比特噪声源，如 $T_1$ 弛豫和 $T_{2\phi}$ 纯退相，只能在二阶引起不对称。利用这些对称性来固定规范，可以系统地识别 SPAM 误差，简化误差表征和缓解。我们在 IBM Kingston 上数值和实验验证了我们的结果。
英文摘要：
Characterizing noise in quantum circuits is fundamentally limited by gauge degrees of freedom; certain parameters, such as the individual contributions of state preparation and measurement (SPAM) errors, are in principle unlearnable from any experiment within the gate set. Here, we show that the physical structure of realistic noise processes imposes approximate symmetry constraints on the Pauli fidelities of gate noise channels. These symmetries relate the fidelity of a Pauli $P$ and its gate-conjugate $U_g P U_g ^{\dagger}$, and can be used to fix the gauge using only knowledge of the error type and not its magnitude. Using Lindbladian perturbation theory, we analyze a broad class of Clifford gates, including $ZZ_{π/2}$, CZ, CNOT, iSWAP, and SWAP, and demonstrate that coherent errors do not induce first-order asymmetry, while only a restricted set of predominantly off-diagonal dissipative errors can break the symmetry at first order, for which we derive simple selection rules. Notably, common single-qubit noise sources such as $T_1$-relaxation and $T_{2ϕ}$-pure-dephasing can only cause asymmetry at second order. Leveraging these symmetries to fix the gauge enables systematic identification of SPAM errors, simplifying error characterization and mitigation. We validate our results numerically and experimentally on IBM Kingston.
